Evaluations of some quadratic Euler sums
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 489-508
https://doi.org/10.4134/BKMS.b190357
Published online August 2, 2019
Printed March 31, 2020
Xin Si, Ce Xu
Xiamen University of Technology; Xiamen University
Abstract : This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.
Keywords : Harmonic numbers, polylogarithm function, Euler sum, Riemann zeta function
MSC numbers : Primary 11M06, 11M32, 33B15
Supported by : This work was co-supported by the National Natural Science Foundation of China (No.41801219), Natural Science Foundation of Fujian Province (No.2019J01849).
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